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Torsions for manifolds with boundary and glueing formulas


Burghelea, D; Friedlander, L; Kappeler, T (1999). Torsions for manifolds with boundary and glueing formulas. Mathematische Nachrichten, 208(1):31-91.

Abstract

We extend the definition of analytic and Reidemeister torsion for closed compact iemannian manifolds, to compact Riemannian manifolds with boundary (M, δ M), given a parallel at bundle F of A-Hilbert modules of finite type and a decomposition of the boundary δM = -M ⊔ δ+M into disjoint components. When F is induced from the universal covering of M, and the fundamental group of M is infinite, these torsions are known as the L2-analytic resp. 2-Reidemeister torsions. If the system (M, δ-M, δ+M, F) is of determinant class we compute he quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of hem. In particular we answer positively Conjecture 7.6 in [LL]. If F is induced from a Γ-principal overing where Γ is a residually finite group, we derive from work of Lück, that the system (M, δ-M, δ+M, F) is of determinant class.

We extend the definition of analytic and Reidemeister torsion for closed compact iemannian manifolds, to compact Riemannian manifolds with boundary (M, δ M), given a parallel at bundle F of A-Hilbert modules of finite type and a decomposition of the boundary δM = -M ⊔ δ+M into disjoint components. When F is induced from the universal covering of M, and the fundamental group of M is infinite, these torsions are known as the L2-analytic resp. 2-Reidemeister torsions. If the system (M, δ-M, δ+M, F) is of determinant class we compute he quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of hem. In particular we answer positively Conjecture 7.6 in [LL]. If F is induced from a Γ-principal overing where Γ is a residually finite group, we derive from work of Lück, that the system (M, δ-M, δ+M, F) is of determinant class.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Torsions;manifolds with boundaries;glueing formulas
Language:English
Date:1999
Deposited On:18 Feb 2010 13:06
Last Modified:05 Apr 2016 13:26
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0025-584X
Publisher DOI:https://doi.org/10.1002/mana.3212080103
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1719799

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